Papers

Radiologists follow heterogeneous reporting practices. Two radiologists examining the same image and identifying the same clinical findings might nevertheless compose superficially distinct reports, varying in terminology, shorthand, formatting, and level of detail. These variations in reporting norms represent an under-appreciated obstacle in efforts to evaluate AI-based radiology report generation (RRG) models, where machine-generated reports are typically assessed based on their concordance with human-generated references. In this paper, we quantify the sensitivity of established evaluation metrics to variations in reporting practices, revealing impacts large enough to alter the rankings of models. We introduce a radiologist-informed taxonomy of variations in radiology reporting practice and a method (ReRef) that rewrites reference reports along the axes of our taxonomy while preserving clinical interpretation. For instance, when comparing the performance of nine RRG models on MIMIC-CXR using RadCliQ-v1, condensing the discussion of normal findings in the reference reports causes Libra to drop from first to second place while CheXOne rises from third to first. Our results suggest that many current metrics fail to decouple clinical interpretation from conformity to reporting practices and that choosing the “right” references that accurately reflect the desired reporting practices can be important in practice. To support future research, we release MIMIC-CXR-Ext-ReRef, a radiologist-validated dataset of 120 (original, alternative) reference report pairs derived from MIMIC-CXR.

The Model Context Protocol (MCP) standardizes communication between autonomous Artificial Intelligence (AI) agents and remote tools over Streamable HTTP. This shift introduces a class of machine-generated, authenticated, and high-frequency JSON-RPC traffic directly into enterprise networks. Enterprise network defenders have historically relied on machine-like cadence as an Indicator of Compromise (IoC). In this study, we show that without explicit network-layer indication, MCP traffic structurally and temporally resembles Command and Control (C2) beaconing behavior, specifically the polling architectures used by advanced persistent threats like Cobalt Strike. Counter to theoretical assumptions about machine-generated polling, our measurements reveal a visibility gap: standard enterprise Intrusion Detection Systems (IDS) and behavioral beacon-scoring frameworks do not classify MCP remote tool usage as anomalous within our testbed scope. Through a controlled Docker-based testbed simulating eleven mathematically defined traffic profiles across three TLS conditions (Opaque, TLS-Inspected, and Cleartext), we evaluate Suricata signature matching and RITA behavioral scoring against MCP JSON-RPC patterns. Our results show that MCP traffic, regardless of temporal smearing (jitter) or TLS inspection visibility, evades detection within this configuration, yielding a consistent 0.0 behavioral beacon score and near-zero IDS content alerts under the Emerging Threats (ET) Open ruleset. While opaque TLS obscures HTTP content, it exposes agent traffic to flow-level temporal analysis; however, NIDS heuristics tuned to identify traditional malware do not flag the lognormal inter-arrival distributions characteristic of generative AI reasoning loops. To address this gap, we propose an agent-native network indication standard including Agent-Native ALPN and standardized out-of-band headers.

Can an attacker turn influence over an artificial intelligence (AI) adviser into a harmful quantum error-correction update? We identify an ambiguity in passive syndrome records that obstructs recovery selection, then show how additional calibration measurements support certified recovery updates under uncertainty and drift. In an odd-distance square toric code with error-free preparation, syndrome measurements, and recovery operations, opposite coherent $X$ rotations produce identical passive syndrome-history distributions. Yet a fixed phase correction can help at one sign and harm at the other. A terminal logical measurement on known encoded calibration states supplies the missing sign information. A separate evaluator accepts an update only when calibration uncertainty and a justified drift bound certify improvement over the current recovery, without assuming that the adviser recommends correctly. In simulated advice attacks, calibration-confidence checks reject harmful proposals while retaining beneficial updates under honest advice. We derive sufficient limits on calibration age that require improvement through deployment. In matched simulations, a validated channel-specific bound retains more beneficial updates than the general bound after accounting for evaluation time, while preventing the tested harmful activations under the stated drift assumption. A separate surface-code experiment includes stochastic circuit faults and noise changing during acquisition. Deterministic controllers achieve at least as many beneficial updates with the same observations. Violating the drift assumption permits harmful acceptance in the toric experiment. The results identify information required for recovery selection, establish conditional guarantees against harmful updates, and quantify the recovery improvements forgone through conservative acceptance.

We study the space complexity of diameter estimation for a set of points in Euclidean space in the dynamic (turnstile) streaming model. The seminal work of Indyk (SODA 2003) gives a $c$-approximation to the Euclidean diameter of $n$ vectors using $n^{O(1/c^2)}$ space. Our main contribution is giving an essentially matching lower bound. Any dynamic streaming algorithm which can $c$-approximate the diameter of $n$ Euclidean vectors must use $n^{\tilde{\Omega}(1/c^2)}$ space.

Large vision-language models have achieved remarkable progress in multi-modal understanding, yet their capabilities in educational settings remain insufficiently evaluated. In AI-assisted language learning, models must interpret artistic imagery, understand its semantic, affective, and cultural content, and reason about visual context to support meaningful interaction. However, existing benchmarks primarily focus on real-world images or domain-specific educational reasoning, providing limited coverage of artistic educational content. To address this gap, we introduce MUSE, a benchmark for evaluating large vision-language models on artistic image understanding in situated educational applications. MUSE decouples image annotation from question generation, enabling diverse tasks with controllable difficulty while reducing annotation effort. It comprises twelve tasks spanning visual perception, semantic and affective interpretation, culture understanding, and compositional reasoning, together with diverse artistic images deliberately curated to center Singaporean and Southeast Asian multicultural contexts alongside Western art traditions, covering multiple themes and difficulty levels. Evaluation of open-source and proprietary models reveals substantial disparities across capability dimensions, particularly in affective interpretation and compositional reasoning. Our analysis further identifies common failure modes and key challenges for developing trustworthy multi-modal models for education. We hope MUSE will serve as a standardized benchmark for advancing multi-modal understanding in situated educational applications.

Kernel methods, and Gaussian Processes (GPs) in particular, require a Hilbertian distance measure—one whose square is conditionally negative definite (CND)—to guarantee positive semi-definiteness (PSD) of the kernel matrix; a condition that fails for many natural input spaces, including smooth manifolds and spaces of probability distributions. We propose the Sparse Landmark Embedding (SLE) kernel, which eliminates this requirement entirely. Each input is embedded into a sparse feature vector via compactly supported bump functions centered at all |D| training points; applying any standard PSD kernel in this embedding space yields a kernel that is provably PSD for arbitrary distance measures. The compact support automatically controls embedding sparsity, keeping kernel matrices well-conditioned and computationally tractable despite the high ambient dimension. We provide theoretical guarantees on PSD, sparsity, stability, and universal approximation, and show that the SLE kernel matches or substantially exceeds domain-specific baselines in both predictive accuracy and uncertainty quantification using geodesic and Wasserstein distances.

As robot capabilities increase, quadratic programming (QP)-based controllers must account for a similarly increasing number of constraints to ensure safe, reliable operation. Yet, with each added constraint, this introduces more chances of momentary conflict: in which case, a QP solver that returns an "infeasible" status leaves the controller with nothing to execute. To address this, we introduce ElastiQP, a modified dual active-set QP solver that relaxes every inequality constraint with an exact, per-constraint l1 penalty while keeping equality constraints (dynamics) hard. Notably, ElastiQP does so by folding the slack variables into the solver analytically, maintaining a constant size of the condensed linear system. On a suite of robot control benchmarks, ElastiQP achieves microsecond-level performance, matching or outperforming leading modern solvers on feasible problems. On infeasible problems, ElastiQP handles these gracefully, confining violations to strictly the conflicting inequality terms, returning a usable solution up to 40x faster than the best alternative solvers. ElastiQP is available as an open-source C++ header-only library, with Python and JAX interfaces, at https://github.com/StanfordASL/elastiqp.

This note establishes a geometric foundation for trajectory-manifold representations of deterministic nonlinear systems in a behavioral setting motivated by data-enabled predictive control. For a discrete-time system $x_{k+1}=f(x_k,u_k)$ with measured state and a $C^r$ transition map, $r\geq 1$, we consider the terminal-state-augmented finite-horizon behavior consisting of all admissible state-input trajectories over a prediction horizon $N$. We prove that this behavior is a $C^r$ embedded submanifold of the ambient trajectory space with intrinsic dimension $n+Nm$, where $n$ and $m$ are the state and input dimensions. Moreover, the rollout map from the admissible initial-state and input coordinates $(x_0,\mathbf u)$ is a $C^r$ diffeomorphism onto the behavior manifold, providing explicit global smooth coordinates. This yields a canonical exact encoder–decoder representation and implies that any exact differentiable latent representation of the full behavior must have latent dimension at least $n+Nm$. The geometric result does not require controllability, stabilizability, or invertibility of the dynamics. Corresponding results are given for zero-order-hold sampled continuous-time systems and fixed-step numerical transition maps. These results provide the deterministic geometric foundation for subsequent data-driven approximation and predictive-control development.

Formal explainability provides mathematically grounded justifications for individual predictions. However, abductive explanations often exceed human cognitive limits by involving too many features, while probabilistic relaxations have remained largely limited to categorical classification. We present a unified framework for probabilistic explainability based on sparse, anchored linear models, applicable to both binary classification and continuous regression. By mapping instances to the Boolean hypercube, our linear explanations strictly generalize subset-based approaches: they capture both the magnitude and direction of feature contributions while enforcing a prescribed sparsity budget $k$. We show that minimizing the relevance error for such explanations is \ClassNPPP-hard when the underlying model is a neural network, and we relate this intractable objective to a tractable surrogate—the fidelity error. For a parameterized family of local distributions, the relevance error of any $k$-sparse explanation is bounded by its fidelity error up to a multiplicative factor that remains small locally. We address the resulting empirical problem using two complementary approaches: a Mixed Integer Programming (MIP) formulation that yields provably optimal empirical solutions while maintaining polynomial sample complexity, and a polynomial-time Iterative Hard Thresholding (IHT) algorithm with provable approximation guarantees. Empirical evaluations show that, unlike state-of-the-art baselines such as LIME and MAPLE, our explanations satisfy both the anchoring and sparsity constraints by construction, while consistently achieving lower relevance error.

The test error of a model plotted against its number of parameters $d$ falls, peaks when the model can just fit the training data, and falls again, exhibiting the double descent phenomenon. We explain the phenomenon with statistical mechanics. The training trajectory of a stochastic gradient-based method is a particle wandering over the energy landscape of the training loss at an induced temperature $T$, and a run that has equilibrated visits every parameter vector of a given training loss equally often, the fundamental postulate of statistical mechanics, with probability given by the Boltzmann distribution. Because training starts at an initial point and has only finite time to diffuse, it carries an effective weight decay, which makes every parameter a quadratic degree of freedom. The equipartition theorem then distributes the energy among the $d$ degrees of freedom in shares of $T/2$, so at a fixed training loss adding parameters lowers the temperature and drives the Boltzmann distribution toward the stationary path. Finally, adding parameters can only lower the $L^2$ norm of the stationary path, so a solution sampled at fixed loss is less likely to be large with increasing $d$, effectively increasing weight regularization.

Reinforcement learning (RL) is an exciting concept as well as a remarkable success story worth sharing. However, RL builds on rather complex interactions between different objects that play out over several cycles. Such dynamics are often best explained with an easily accessible implementation. We present RLLBC-Lib, a carefully crafted code library with the goal of lowering the entry barrier for students and other learners of RL in the context of learning-based control. At its heart, RLLBC-Lib comprises a comprehensive library of tabular RL approaches to enforce a clear understanding of the theoretical foundations. A deep RL library follows the same design principles, underscoring the parallels between simple tabular and state-of-the-art deep RL approaches. Additionally, RLLBC-Lib provides a collection of implementations illustrating core RL principles and contrasting RL to other learning-based control approaches. Finally, RLLBC-Lib provides an ideal basis for creating programming assignments with automated grading.

The theoretical foundation for model checking timed systems against Metric Interval Temporal Logic (MITL) was established in the early 1990s, yet the first practical tool supporting future MITL (MightyL) did not emerge until 2017. Recently, there has been growing interest in extending this toolchain to support more expressive logical operators, including past modalities, Pnueli modalities, and limited use of singular intervals. MightyPPL is one such toolchain. We introduce an upgraded version of MIghtyPPL that enables for the first time, the model checking of Metric Temporal Logic (MTL) properties of the form (whenever an event p occurs, it is eventually followed by some event q after exactly some k time units) in addition to Pnueli and Past modalities. We discuss the tool's underlying architecture and implementation, and present a performance evaluation against the Tempora tool across diverse satisfiability and model checking benchmarks, demonstrating that MightyPPL delivers significantly better performance.

Adults with intellectual and developmental disabilities (IDD) are increasingly transitioning from family homes towards semi-inde\-pendent living. As parents hand off the role of primary caregiver, they face numerous challenges in arranging consistent and quality support. Our research centers on understanding these caregiving routines. By focusing on the unique lived experience of parents, who possess extensive explicit and tacit knowledge of their adult child's requirements, we aim to map the management of care they provide. This foundational understanding is essential to identifying how assistive technologies can effectively serve a key role in supporting adults with IDD in this transition. In this work, we interviewed 16 parents of adults with IDD beginning this transition to understand: 1) how they currently provide support for daily living and what makes their support effective; 2) what their experiences and perceptions are regarding the use of technology; and 3) how they envision assistive technology successfully integrating with their adult child's new home or with other supports to promote independence. Our thematic analysis produced four themes: common modes of support, inside the routine to support growth, the fragility of continuity of care across transitions, and participants' perceptions and experiences of assistive technology. Building on these findings, we derive four design principles for growth-oriented assistive technology. These include pre-transition onboarding to capture caregiver tacit knowledge; structured scaffolding towards long-term growth; adaptive sensing that responds to day-to-day variability; and customization for the individual balanced with consistency for the care network.

A game character should not have to reread its entire life before every conversation. For locally deployed language-model characters, however, revising a few memories can invalidate a long reusable prefix. The resulting preparation cost competes with both foreground dialogue and the maintenance of other characters. This matters especially when dialogue feeds game-defined actions and value judgments: a fluent but incorrect account of who owns an item, or whether a transfer has already happened, can corrupt the input to otherwise deterministic rules. We study incremental memory maintenance for long-lived game NPCs in a quantized Qwen hybrid recurrent-attention model. Our runtime removes superseded attention KV entries, computes replacement records at the true sequence tail, and preserves the continuing recurrent state and unchanged KV. Existing local experiments combine multi-update dialogue replays, fixed-input placement ablations, and attention diagnostics. Independent block composition weakens query-conditioned memory selection without a uniform chunk-initial attention collapse. True-tail updates preserve important current-state and historical bindings across eight scripted maintenance rounds; a placement case recovers the full-refill quantity in three reconstructions, while slot-preserving alternatives repeat a double-subtraction error. Attention-distribution proximity alone does not explain these semantic differences. The results motivate treating a character's inference state as a maintained, history-dependent resource, rather than only a disposable encoding of its latest memory text.

Function-as-a-Service (FaaS) has emerged as the prominent programming model for the edge-cloud continuum. FaaS inherently decouples stateless functions from their persistent state. We study how to jointly schedule functions and place data to minimize client latency, considering data replication under heterogeneous consistency requirements. We introduce a Binary Linear Programming (BLP) model to compute optimal placements, establishing a rigorous theoretical baseline. Since the BLP scales cubically with the infrastructure nodes, we propose a topology-aware greedy heuristic that efficiently approximates the optimal solution. Our evaluation shows that the heuristic achieves near-optimal placement quality at a fraction of the computational cost, making it suitable for periodic system reconfigurations.

In this work, we present a computational model to investigate transdermal insulin delivery using coated microneedles. A detailed skin geometry incorporating a coated microneedles was developed to analyze insulin release through the different skin layers and to evaluate the influence of key transport parameters. The model represents the major skin layers: the stratum corneum, viable epidermis, and dermis. Unstructured grids were used to achieve a reliable resolution of the model. The simulations provide insights into the permeation of insulin from the coated microneedles and the transport and distribution across the different skin layers. Finally, the simulation results were compared with experimental data to evaluate the predictive capability of the model.

Bipedal loco-manipulation enables robots to interact with objects beyond the nominal workspace of their arms by coordinating locomotion and manipulation. Realizing this capability requires a low-level whole-body controller that translates task-level manipulation goals into coordinated arm and leg motions while maintaining balance. We present a unified whole-body controller trained with reinforcement learning that directly maps 6-DoF end-effector targets to coordinated actions for the bipedal base and robotic arm. Given only an end-effector target, the learned controller autonomously coordinates reaching, postural adaptation, and stepping without explicit base-velocity or footstep commands. A reward-gating strategy regulates the trade-offs among end-effector tracking, locomotion, and balance during training, while a temporal context estimator combines windowed Transformer encoding, recurrent GRU memory, and auxiliary dynamics prediction to extract dynamics-relevant information from observation history. Real-robot experiments demonstrate that the same controller supports reaching, postural adaptation, and stepping under commands from VR teleoperation, a learned diffusion policy, and scripted trajectories, providing a common end-effector interface for diverse manipulation tasks.

In multi-agent environments, coordinating agents to prevent interference and ensure robust individual performance is a critical challenge. Previous research on social laws for multi-agent systems has primarily focused on deterministic, goal-based settings. This paper extends the concept of social laws to stochastic, reward-based environments, proposing a formalism for defining and verifying their robustness under various conditions. We introduce the notion of $\alpha$-robustness, a measure of the guaranteed utility each agent retains while pursuing its optimal single agent policy, assuming all agents obey the social law. We then present an approach for robustness verification of social laws in stochastic settings, based on a reduction to solving a series of Markov decision processes. Empirical evaluations on toy environments illustrate the potential of our framework.

In particle collider experiments, event reconstruction is the task of inferring the kinematics of short-lived particles produced in the hard scatter from the stable final states recorded by detectors. We decompose event reconstruction into two primary tasks: assigning measured jets and charged leptons to parent particles, and predicting unmeasured neutrino kinematics. We present VyPER, a novel geometric learning framework that represents collider events as hypergraphs with a physics-inspired topology. VyPER combines the supervised classification of hyperedges for particle assignment with a diffusion model for predicting neutrino kinematics, leveraging a joint loss function to optimize both reconstruction tasks within a unified framework. We showcase VyPER across several proton-proton collision processes, comparing its performance to existing analytical and machine-learning-based reconstruction techniques. In doing so, we demonstrate that accurate event reconstruction is achievable across a diverse range of Standard Model physics processes, opening new avenues for precision measurements in the Higgs boson, electroweak, and top-quark sectors.

This paper establishes the necessary and sufficient conditions for asymptotic stability of the time-varying Kalman filter applied to a linear time invariant system with semidefinite initial state covariance and positive definite process and measurement noise. Rather than analyze the discrete Riccati equation as in the classic literature, the equivalent state smoothing optimization problem is stated and all results are established using properties of this optimization problem. A Lyapunov-like function, termed a modified $Q$-function is derived and used for this analysis. This optimization approach removes the need for the classic but cumbersome Riccati iteration algebra and provides better generalization and application for nonlinear systems.

Function-as-a-Service (FaaS) is a widely adopted paradigm to simplify application deployment across the edge-to-cloud continuum. However, its stateless nature forces functions to retrieve their state from external, typically cloud-centric, data stores, reintroducing the very latency that edge computing aims to eliminate. This issue is further exacerbated by location-agnostic schedulers and rigid, one-size-fits-all consistency models that fail to capture the diverse requirements of edge applications. In this paper, we propose Ermes, a distributed platform that natively integrates state management into the FaaS paradigm, enabling the joint distribution of computational workloads and application state across the edge-to-cloud continuum. Ermes organizes application state into logical units, termed collections, and employs a distributed coordination algorithm that jointly maps collections and functions onto the available nodes seeking to minimize the latency perceived by the clients. In addition, it supports fine-grained replication and per-collection consistency levels, ranging from sequential to eventual consistency, leaving developers the choice of how to resolve the trade-off between consistency and performance. The experimental evaluation shows that Ermes quickly turns remote state accesses into local ones and sustains low latency as the workload grows, and as clients move across the edge.

Physical properties, such as friction, hardness, stiffness, and density, govern how robots should grasp, manipulate and interact with objects, yet estimating these properties from RGB images remains challenging. Existing methods typically employ per-object reconstruction augmented with physical properties or directly query vision-language models at test time, which results in substantial computational overhead that limits their applicability. In this work, we present PhysVGGT, a feed-forward model that predicts dense maps of friction coefficient, Shore hardness, Young's modulus, and density, together with object-level mass, from a single RGB image in one forward pass. The key idea of PhysVGGT is to formulate physical property estimation as a dense per-pixel prediction problem and employ a visual geometry transformer to extract geometry-aware tokens from the input image followed by a dense prediction branch for estimating local physical properties and a global prediction branch for estimating object-level mass. In addition, we introduce a scalable pseudo-label generation pipeline that enables large-scale weakly supervised training for dense physical property prediction, substantially reducing the need for expensive direct physical measurements. Extensive experiments show that PhysVGGT achieves state-of-the-art performance on the ABO-500 dataset and generalizes effectively to the out-of-distribution NeRF2Physics dataset. Moreover, PhysVGGT eliminates the need for per-object reconstruction and test-time optimization, achieving an inference latency of only 0.13s per image, making it $27\times$ faster than the previous state of the art.

Taming the exponential increase of the Hilbert space dimension with system size in the simulation of gapped quantum lattice models is of the highest relevance for understanding and designing exotic quantum materials, where nonlocal interactions are of particular interest. High-order linked-cluster expansions provide access the solution of the eigenvalue problem for the infinite system, yet rely on the computation of high-dimensional oscillatory lattice sums with a graph structure, only approachable with Monte Carlo methods so far. This work resolves this issue, rendering all required graph lattice sums, referred to as graph zeta functions for kernels involving power-laws, computable. The resulting method reduces the evaluation time for state-of-the art series expansions from tenthousands of core-hours to minutes. After factorizing the lattice sum over blocks, each block is evaluated by the cheapest available strategy depending on its treewidth $\mathrm{tw}$. Basic blocks admit analytic forms in terms of generalized zeta functions. Series-parallel blocks with $\mathrm{tw}\le 2$ can be computed at linear cost in the number of graph nodes and in the size of the momentum grid using a semi-analytical algebra based on Epstein zeta functions and rapidly decaying Fourier series. Finally, for $\mathrm{tw}>2$, the method is combined with tensor-network bucket elimination yielding polynomial scaling of numerical work and memory in momentum grid size with exponents only growing with $\mathrm{tw}$ rather than with the number of vertices. Through use of FFT, the full momentum grid is recovered at the cost of a single momentum evaluation. We provide a detailed analysis of the precision and runtime of our method against analytic and numerical benchmarks. We further reproduce published Monte Carlo data for the transverse-field Ising model on different 1D, 2D, and 3D lattices, obtaining full agreement.

Mixture-of-Experts (MoE) language models suffer from large parameter counts, which create a significant memory bottleneck. Expert pruning is the most direct approach for reducing this parameter count, yet existing methods make pruning decisions for each expert independently, and assume experts' contributions are purely additive. In reality, expert usage in MoEs is inherently cooperative. We derive HOPE (Higher-Order Pruning of Experts), a second-order pruning objective which provably minimizes an upper bound on the error resulting from pruning. We show that REAP (a state-of-the-art first-order pruning method) is a special case of HOPE where interaction terms are ignored. Across three frontier MoE models (up to 122B parameters), two distinct calibration sets, and multiple benchmarks (including math, instruction following, coding, and an agentic suite), we demonstrate that HOPE produces better pruning decisions than existing methods, and its advantage is most pronounced at high pruning rates and on challenging agentic workloads. At 50% pruning, HOPE outperforms all baselines and achieves an average rank of 1.58 out of 5 methods (versus 2.42 for the next-best method, REAP), with gains of up to +6.1% on agentic coding. Over all conditions, HOPE again achieves the best average rank and surpasses every other method in the majority of head-to-head comparisons. By preserving cooperative expert structure that first-order methods ignore, HOPE enables aggressive compression with minimal degradation, particularly on complex tasks where diverse expert combinations are invoked over long sequences.

The Matrix Spencer conjecture asks whether any $n$ real symmetric matrices A_1,...,A_n \in \mathbb{R}^{m \times m} of operator norm at most one admit a signing $x\in\{-1,1\}^n$ such that the operator norm of the signed sum is at most O(\sqrt{n \log(2m/n)}) We give a randomized algorithm establishing this bound with polynomial runtime in the real-arithmetic model. We first prove the $O(\sqrt n)$ bound for $m\le n$, resolving the square case, and then obtain the rectangular bound by changing the regularizer. As in earlier algorithmic discrepancy methods \cite{lovettmeka2012,bansalLaddhaVempala2022,pesentivladu2026}, we run a covariance-controlled random walk from the origin of the hypercube, rounding coordinates near its faces and keeping them fixed. Our potential measures a soft spectral edge of the evolving discrepancy matrix perturbed by an operator-valued free semicircular element. Inspired by the free interpolation approach of \cite{bbvh2023}, we combine Lehner's variational formula for the free edge \cite{lehner1999} with spectral Tsallis regularization \cite{allenZhuLiaoOrecchia2015,pesentivladu2026}. This puts the discrepancy and remaining covariance in a single smooth optimization problem. The potential has a finite-dimensional semidefinite formulation. Stability of its optimizer, governed by equations related to the matrix Dyson equation \cite{erdos2019}, lets us find a large subspace in which to move while controlling discrepancy. The square case uses the Tsallis–$1/2$ regularizer; the rectangular case uses a suitable generalized Tsallis power regularizer. Our companion paper \cite{kathuria2026ks} applies these ideas to give an algorithmic proof of Weaver's discrepancy theorem, whose existence proof by [MSS15] resolved the Kadison–Singer conjecture \cite{mss2015}.Lean formalizations of our main discrepancy theorems have been completed and will be released shortly.

\cite{mss2015} proved Weaver's discrepancy result existentially, resolving the Kadison–Singer conjecture . Finding such signs efficiently for general inputs remained an open algorithmic question. In the real-arithmetic model, we give a deterministic algorithm running in polynomial time with discrepancy at most $35\sqrt\varepsilon$. The algorithm walks from the origin of the hypercube to a vertex, fixing coordinates as they hit a face. Its potential measures a soft spectral edge of the discrepancy matrix perturbed by an operator-valued free semicircular element. The perturbation's covariance vanishes as the coefficients reach their endpoints. Inspired by the free interpolation approach of Bandeira, Boedihardjo, and van Handel \cite{bbvh2023}, we combine Lehner's variational formula \cite{lehner1999} with spectral Tsallis–$1/2$ regularization used in \cite{allenZhuLiaoOrecchia2015} and \cite{pesentivladu2026}. The resulting potential has a finite-dimensional SDP formulation, allowing the discrepancy and remaining covariance to be analyzed together. We analyze the optimizer's stability through the linearized Karush–Kuhn–Tucker (KKT) system of a regularized min–max problem, whose stationarity equations are related to the matrix Dyson equation \cite{erdos2019}. This gives the movement rule: either a coordinate can move toward its nearer endpoint at small spectral cost, or a low-curvature direction orthogonal to the current coefficient vector allows further progress. Choosing the better sign of this direction controls discrepancy while increasing the squared distance from the origin. Upcoming work \cite{kathuria2026higherRank} will address higher-rank Kadison-Singer and spectrally thin trees. Lean formalizations of our main discrepancy theorems have been completed and will be released shortly.

Conventional motion planning treats collision as a binary constraint, although contact with different objects can have drastically different consequences. A robot may safely brush against a cardboard box while even minor contact with a glass, laptop, or unstable object may be undesirable. Moreover, a direct robot–object collision can move the contacted object and trigger secondary object–object collisions, making the risk of a motion depend on the physical evolution of the scene rather than only on the robot's geometric path. We present CaSCo, a cascade-aware soft-collision motion planning framework in which a vision-language or language model assigns semantic risk to objects and a physics simulator predicts the consequences of candidate robot motions. CaSCo searches for a path that minimizes the total semantic risk of the unique objects displaced either directly by the robot or indirectly through cascaded collisions. Because collisions change the environment, we augment roadmap states with the predicted object arrangement and the set of objects whose risk has already been incurred. We develop an optimal graph-search algorithm with an admissible and consistent cascade-relaxed heuristic and caching and pruning mechanisms for efficient search. Experiments in cluttered manipulation environments evaluate semantic risk, cascade reasoning, planning efficiency, and real-robot operation.

Agent benchmarks are substantially more costly to evaluate than conventional LLM benchmarks. Benchmark compression is therefore a natural solution, yet existing methods primarily model redundancy in task–model final-score distributions, which is important in agentic evaluation. To address this limitation, we analyze large-scale trajectories and identify six complementary process signals that are systematically associated with final agent performance. To disentangle agent performance redundancy from a complete perspective, we propose DualViewEval, an agent benchmark compression method that jointly exploits outcome and process relations to learn an exact-size miniset and predict the full-benchmark scores. Across five agent benchmarks and five representative baselines, DualViewEval achieves the best results in all datasets. With only 20 tasks, it achieves $24\times$–$40\times$ compression on APEX-Agents and BFCL, reducing mean absolute error (MAE) by $14.5\%$–$28.2\%$ over the strongest competitors while improving Kendall's $\tau$ by up to $7.2\%$ relative to EssenceBench on SWE-bench Verified. The selected minisets further reveal capability differences among different agents, providing compact and diagnostic feedback for efficient agentic model development.

Existing legal benchmarks cover diverse tasks, while continuous monetary remedies remain comparatively underexplored. We introduce ECtHR-NPD, to the best of our knowledge, the first benchmark for predicting non-pecuniary damage (NPD) awards at the European Court of Human Rights (ECtHR) from case information when no statutory formula or explicit calculation rule determines the amount. ECtHR-NPD contains 14,575 cases with case-level awards in nominal euros, chronological splits, and a protocol separating target construction from model input. We evaluate a battery of methods, including constant predictors, gradient-boosted trees, retrieval methods, fine-tuned encoder language models (LMs), prompted decoder LMs, and knowledge-augmented agents. Our results show that more sophisticated LM and agentic approaches do not consistently outperform the strongest feature-based baseline. All model families struggle to identify zero awards and to calibrate high-award predictions, with further degradation on the Challenging test view, making ECtHR-NPD a challenging testbed for current state-of-the-art open-weight and proprietary LMs.

Health discourse in social media videos often contains densely entangled claims spanning multiple thematic aspects, stances, evidential frames, and rhetorical functions within short conversational spans. Existing approaches largely rely on coarse topic-level, sentiment-based, or stance-oriented representations that do not adequately capture this structure. Our analysis identifies an average of 13.22 atomic claims per minute, motivating richer claim-level discourse representations. We introduce a structured framework for claim-level discourse analysis in dense health narratives. Our framework models discourse through tuples linking atomic claims with thematic aspects, stance, and multidimensional pragmatic discourse attributes. To support this setting, we construct a benchmark spanning four health domains with 1,191 manually annotated claims from 60 videos. Using this framework, we evaluate automated structured discourse analysis under different discourse context settings. Results show that current LLMs achieve strong performance on thematic categorization and stance prediction, but struggle with high-dimensional pragmatic profiling. We also find that different discourse tasks benefit from different forms of contextual reasoning, suggesting that future systems may require task decomposition and specialized inference strategies.